EVALUATE RADICAL EXPRESSIONS

Evaluate the following expressions using the given values of the variables.

Example 1 :

√x + √y for x = 4 and y = 9

Solution :

= √x + √y

Substitute x = 4 and y = 9.

= √4 + √9

= 2 + 3

= 5

Example 2 :

2√(185 - x) for x = 169

Solution :

= 2√(185 - x)

Substitute x = 169.

= 2√(185 - 169)

= 2√16

= 2√(4 ⋅ 4)

= 2(4)

= 8

Example 3 :

5√x³ for x = 3

Solution :

= 5√x³

Substitute x = 3.

= 5√3³

= 5√(3 ⋅ 3 ⋅ 3)

= 5(3√(3)

= 15√3

Example 4 :

5√x + 1 for x = 1

Solution :

= 5√x + 1

Substitute x = 1.

= 5√1 + 1

= 5√1 + 1

= 5(1) + 1

= 5 + 1

= 6

Example 5 :

√(x/49) for x = 25 

Solution :

= √(x/49)

Substitute x = 25.

= √(25/49)

= √25/√49

= √(5 ⋅ 5)/√(7 ⋅ 7)

= 5/7

Example 6 :

√(x² + y²) for x = 3 and y = 4

Solution :

= √(x² + y²)

Substitute x = 3 and y = 4.

= √(3² + 4²)

= √(9 + 16)

= √25

= √(5 ⋅ 5)

= 5

Example 7 :

³√x - ³√y for x = 27 and y = 8

Solution :

³√x - ³√y

Substitute x = 27 and y = 8.

= ³√27 - ³√8

= 3 - 2

= 1

Example 8 :

√12w + √27w for w = 3

Solution :

= √(12w) + √(27w)

= √(2 ⋅ 2 ⋅ 3 ⋅ w) + √(3 ⋅ 3 ⋅ 3 ⋅ w)

= 2√3w + 3√3w

= 5√3w

Substitute w = 3.

= 5√(3 ⋅ 3)

= 5(3)

= 15

Example 9 :

³√8x³y⁶ + √9x²y⁴ for x = 1 and y = 2

Solution :

= ³√8x³y⁶ + √9x²y⁴

= ³√(2 ⋅ 2 ⋅ 2 ⋅ x ⋅ x ⋅ x ⋅ y² ⋅ y² ⋅ y²) + √(3 ⋅ 3 ⋅ x ⋅ x ⋅ y² ⋅ y²)

= 2xy² + 3xy²

= 5xy²

Substitute x = 1 and y = 2.

= 5(1)(2²)

= 5(1)(4)

= 20

Example 10 :

√4p²q⁴ - ³√125p³q⁶ for p = -2 and q = -3

Solution :

= √4p²q⁴ - ³√125p³q⁶

= √(2 ⋅ 2 ⋅ p ⋅ p ⋅ q² ⋅ q²) - √(5 ⋅ 5 ⋅ 5 ⋅ p ⋅ p ⋅ p ⋅ q² ⋅ q² ⋅ q²)

= 2pq² - 5pq²

= -3pq²

Substitute p = -2 and q = -3.

= -3(-2)(-3)²

= -3(-2)(9)

= 54 

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